Question 1148413
{{{ 8^( x + 4 ) = 16^( 4x - 3 ) }}}
{{{ ( 2^3 )^( x + 4 ) = ( 2^4 )^( 4x - 3 ) }}}
Use the rule:
{{{ ( a^b )^c = a^( b*c ) }}}
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{{{ 2^( 3*( x + 4 ) ) = 2^( 4*( 4x - 3 ) ) }}}
{{{ 3*( x + 4 ) = 4*( 4x - 3 ) }}}
{{{ 3x + 12 = 16x - 12 }}}
{{{ 13x = 24 }}}
{{{ x = 24/13 }}}
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check:
{{{ 8^( x + 4 ) = 16^( 4x - 3 ) }}}
{{{ 8^( 24/13 + 52/13 ) = 16^( 4*(24/13) - 39/13 ) }}}
{{{ 8^( 76/13 ) = 16^( 96/13 - 39/13 ) }}}
{{{ 8^( 76/13 ) = 16^( 57/13 ) ) }}}
{{{ 2^( 3*(76/13)) = 2^( 4*(57/13)) }}}
{{{ 2^( 228/13 ) = 2^( 228/13 ) }}}
OK
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